Popa Algebras in Free Group Factors
نویسندگان
چکیده
For each 1 < s < ∞, a Popa algebra As is constructed that embeds as a weakly dense C∗–subalgebra of the interpolated free group factor L(Fs). Certain approximation properties for As are shown. It follows that L(Fs) has the weak expectation property of Lance with respect to As. In the course of the demonstration, it is proved that under certain conditions, full amalgamated free products of matrix algebras are residually finite dimensional.
منابع مشابه
Free Entropy Dimension in Amalgamated Free Products
We calculate the microstates free entropy dimension of natural generators in an amalgamated free product of certain von Neumann algebras, with amalgamation over a hyperfinite subalgebra. In particular, some ‘exotic’ Popa algebra generators of free group factors are shown to have the expected free entropy dimension. We also show that microstates and non–microstates free entropy dimension agree f...
متن کاملClassification of Strongly Free Actions of Discrete Amenable Groups on Strongly Amenable Subfactors of Type Iii0
In the theory of operator algebras, classification of group actions on approximately finite dimensional (AFD) factors has been done since Connes’s work [2]. In subfactor theory, various results on classification of group actions have been obtained. The most powerful results have been obtained by Popa in [16], who classified the strongly outer actions of discrete amenable groups on strongly amen...
متن کاملAmalgamated Free Product over Cartan Subalgebra
Amalgamated free products of von Neumann algebras were first used by S. Popa ([26]) to construct an irreducible inclusion of (non-AFD) type II1 factors with an arbitrary (admissible) Jones index. Further investigation in this direction was made by K. Dykema ([10]) and F. Rădulescu ([27, 29]) based on Voiculescu’s powerful machine ([40, 41, 44]), and F. Boca ([4]) discussed the Haagerup approxim...
متن کاملDeformation and rigidity for group actions and von Neumann algebras
We present some recent rigidity results for von Neumann algebras (II1 factors) and equivalence relations arising from measure preserving actions of groups on probability spaces which satisfy a combination of deformation and rigidity properties. This includes strong rigidity results for factors with calculation of their fundamental group and cocycle superrigidity for actions with applications to...
متن کاملIndecomposability of Free Group Factors over Nonprime Subfactors and Abelian Subalgebras
Abstract. We use the free entropy defined by D. Voiculescu to prove that the free group factors can not be decomposed as closed linear spans of noncommutative monomials in elements of nonprime subfactors or abelian ∗-subalgebras, if the degrees of monomials have an upper bound depending on the number of generators. The resulting estimates for the hyperfinite and abelian dimensions of free group...
متن کامل